Question

Calculate the number of free electrons per cubic meter for silver, assuming that there are 1.3 free electrons per silver atom. The electrical conductivity and density for Ag are 6.8 × 107(Ω.m)–1and 10.5 g/cm3, respectively.

Answer 1

Answer : The number of free electrons per cubic meter for silver are $7.62\times 10^{28}m^{-3}$

Explanation :

To calculate the number of free electrons per cubic meter for silver by using the following equation:

$n=1.3\times N_{Ag}$

$n=1.3\times \frac{\rho_{Ag}\times N_A}{A_{Ag}}$

where,

$\rho_{Ag}$ = density of Ag = $10.5g/cm^3$

$N_A$ = Avogadro's number = $6.022\times 10^{23}atoms/mol$

$A_{Ag}$ = 107.87 g/mol

Now put all the given values in the above formula, we get:

$n=1.3\times \frac{\rho_{Ag}\times N_A}{A_{Ag}}$

$n=1.3\times \frac{(10.5g/cm^3)\times (6.022\times 10^{23}atoms/mol)}{107.87g/mol}$

$n=7.62\times 10^{22}cm^{-3}$

$n=7.62\times 10^{28}m^{-3}$

conversion used : $1cm^{-3}=10^6m^{-3}$

Therefore, the number of free electrons per cubic meter for silver are $7.62\times 10^{28}m^{-3}$